The dispersion of chemicals or pollutants plays an important role in many geophysical processes, including for dynamics of the climate. Flows in the oceans and the atmosphere are in a strongly turbulent state, which is sensitive to both the stable density stratification and to the planetary rotation. This provides a strong motivation to investigate the fundamental properties of these flows and, in particular, of the interplay between kinetic and potential energy modes. This thesis is devoted to these problems and focuses on the motion of fluid tracers transported by turbulence in the presence of rotation and stratification. Specifically, we analyze trajectories of tracers obtained from simulations of the incompressible Boussinesq equations. We developed highly efficient octree-based algorithms to identify and study groups of particles given an initial relative distance r. By measuring how these groups of particles separate, we quantified their dispersion and documented the manifestation of the flow irreversibility. Moreover, we studied the dependence of the initial orientation on the growth of relative distances and observed non-Gaussian, intermittent statistics of pair dispersion. By tracking the motion of fluid particle pairs both forwards and backwards in time, we studied the exchange between their relative kinetic and potential energies and observed that the average direction of this exchange depends on the distance between the particles. At small distances, potential energy tends to be converted into kinetic energy. For larger separations between the particles, a transfer with the opposite sign prevails. Remarkably, the length scale where the sign switch occurs, aligns with the characteristic length scale of the stratification layers, at least as long as turbulence is mostly due to the motion of vortices. Furthermore, we studied how the presence of rotation and stratification modifies the coarse-grained velocity gradient tensor and explored the implications for the deformation of fluid volumes.
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Disciplines